Let $A \in M_p(\mathbb{C})$ be nilpotent of order $k$. Let $x \in \mathbb{C}$. Show that $E\left(xI_p + A\right)$ exists and that $E\left(xI_p + A\right) = e^x E(A)$.
Let $A \in M_p(\mathbb{C})$ be nilpotent of order $k$. Let $x \in \mathbb{C}$.
Show that $E\left(xI_p + A\right)$ exists and that $E\left(xI_p + A\right) = e^x E(A)$.